FIXED POINT THEORY AND ITERATIVE PROCEDURES: FROM CLASSICAL THEOREMS TO MODERN DEVELOPMENTS

Abstract

The notion of fixed point theory is the key of nonlinear analysis in a specific way as it composes prominent tools to find existence and uniqueness of solutions in number of non linear problems and also provide methods to find solutions of these problems. The main idea behind the work on fixed point theory is a way to recognize conditions to be applied on the space or on the map or both simultaneously that will ensure fixed point. The paper purposes to provide a comprehensive review of classical and modern fixed point theorems and their applications to more general spaces, with a particular focus on iterative procedures. The review will cover fundamental concepts and techniques of fixed point theory, as well as recent developments in this field.